The present invention relates to three-dimensional (3D) computerized tomography (CT) and, more particularly, methods and systems providing complete data scanning paths on the surface of a sphere.
In conventional computerized tomography for both medical and industrial applications, an x-ray fan beam and a linear array detector are employed. Two-dimensional (2D) imaging is achieved. While the data set is complete and image quality is correspondingly high, only a single slice of an object is imaged at a time. When a 3D image is required, a stack of slices approach is employed. Acquiring a 3D data set one 2D slice at a time is inherently slow. Moreover, in medical applications, motion artifacts occur because adjacent slices are not imaged simultaneously. Also, dose utilization is less than optimal, because the distance between slices is typically less than the x-ray collimator aperture, resulting in a double exposure to many parts of the body.
In 2D CT, the scanning path of the source is often a simple circular scan about the object. The linear array detector is fixed relative to the source. (Although it is usual to talk about a scan path of a source relative to the object to be imaged, it is to be appreciated that the object may be rotated or otherwise moved to provide relative motion between the object and the source.)
To avoid the slowness of the 2D stack of slices approach for 3D imaging, some systems employ true cone beam geometry for 3D imaging. In such systems, a cone beam x-ray source and a 2D area detector are used. An object is scanned, preferably over a 360.degree. angular range, either by moving the x-ray source in a scanning circle around the object or by rotating the object while the source remains stationary. In either case, the area detector is fixed relative to the source. The relative movement between the source and object which is to be imaged provides scanning in either case. Compared to the 2D stack of slices approach to achieve 3D imaging, the cone beam geometry has the potential to achieve rapid 3D imaging of both medical and industrial objects with improved dose utilization.
The standard scanning path used in cone beam 3D CT imaging is a single circle scan of source and detector around the object. However, the data acquired in a single scanning circle can be shown to be incomplete for 3D CT imaging.
Complete data scanning paths are known for 3D CT, but they often provide complete data at the expense of implementation complexity or impracticality. For example, two perpendicular circle scans around the object to be imaged provide complete data, but such scans cannot be readily implemented on standard computerized numerical controllers (CNC). U.S. Pat. No. 5,073,910 issued Dec. 17, 1991 to the present inventors discloses a complete data scanning path. Further, U.S. patent application Ser. No. 07/992,673, filed on concurrently herewith, in the name of one of the present inventors, Jeffrey W. Eberhard, discloses various complete data cone beam 3D scanning paths. The patent application and the patent, both of which are assigned to the assignee of the present application, are hereby incorporated by reference. No representation is being made that the subject matter of the patent application and patent are necessarily prior art to the present application. (Moreover, it is expressly noted that U.S. patent application Ser. No. 07/992,673, docket, discloses one embodiment of the present invention in connection with its description of techniques for setting sampling intervals or steps in various data scanning paths.)
The criteria for data set completeness relative to scanning path in a 3D CT system are described in the paper by Bruce D. Smith entitled "Image Reconstruction From Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods", IEEE Transactions on Medical Imaging, Volume MI-4, No. 1, pages 14-25 (March 1985), hereby incorporated by reference.
The above-mentioned Eberhard et al. U.S. Pat. No. 5,073,910 patent discloses, among other things, complete data scanning paths on the surface of a cylinder. Although such data scanning paths are generally quite useful, it would also be helpful to have further complete data scanning paths. Moreover, there is a lack of uniformity of Radon space filling in connection with the scanning paths on the surface of a cylinder. Such cylindrical scanning paths require a relatively large number of steps to calculate the Radon transform of the cone beam data set.